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Sumario:The antineutron-proton total cross section has been measured in the low momentum range 50-400 MeV/c (below 100 MeV/c for the first time). The measurement was performed at LEAR (CERN) by the OBELIX experiment, thanks to its unique antineutron beam facility. A thick target transmission technique has been used. The measured total cross section shows an anomalous behaviour below 100 MeV/c. A dominance of the isospin I=0 channel over the I=1 one at low energy is clearly deduced. (28 refs).